Resistivity and its Dependence Upon Temperature

What is Resistivity?

Resistance of one meter cube of a material is called resistivity or specific resistance. It is denoted by (rho) ρ.

The Resistivity of Different Materials

MaterialResistivity ρ (ohm.m)
Coppe, Annealed1.72×10-8
Aluminium2.65 x10-8
Manganin48.2 x10-8
Nichrome (Ni.Fe.Cr)100 x10-8
Carbon* (graphite)3-60×10-5
Quartz (fused)7.5×1017
Hard rubber1-100×1013

Resistivity Formula

At constant temperature:

  • Resistance is directly proportional to length.
  • Resistance is inversely proportional to area.

R ∝ L

R ∝ 1/A

R ∝ L/A

R ∝ ρ L/A    or    ρ = RA/L

Unit: ρ = RA/L  =  Ω-m2/m  = Ω.m

Resistivity Unit

The unit of resistivity is:

CGS unitΩ.cm
SI unitΩ.m
Dimension of resistivityM1L3T-3A-2

Difference Between Resistance and Resistivity

Resistance is the characteristics of a particular wire where as resistivity is the property of the material of the wire.

Resistance is the property of a material that opposes the flow of electric current through itResistivity is the inherent property of a material that describes how strongly it resists the flow of electric current
Represented by the letter R and its unit of measurement is ohms (Ω)It is represented by the Greek letter ρ (rho) and its unit of measurement is ohm-meters (Ω·m)
Resistance depends on the dimensions and shape of the conductor, as well as its temperature and the type of material it is made ofResistivity is an intrinsic property of a material that does not depend on its dimensions or shape
The formula for calculating resistance is R = V/I, where V is voltage and I is currentThe formula for calculating resistivity is ρ = RA/L, where R is resistance, A is the cross-sectional area of the conductor, and L is its length
Resistance is a scalar quantityResistivity is a tensor quantity

Related material:

Resistivity Dependence on Temperature

The resistivity ‘ρ’ of a material depends upon its temperature.

Resistance of material is due to the collision of free electrons with atoms of lattice. As temperature rises collisions increase and hence resistance also increases.

Experimentally it is found that the change of resistance of a wire is nearly linear over a wide range of temperatures above and below 0oC.


α = (Rt – Ro)/(Rot)


  • Ro = Resistance of conductor at 0oC
  • Rt = Resistance of conductor at toC
  • Rt – Ro = Change in resistance
  • t = Rise in temperature

Experimentally, It is found that

Rt – Ro ∝ Ro

Rt – Ro ∝ t

Rt – Ro ∝ Rot

Rt – Ro = ∝Rot

∝ = (Rt – Ro)/(Rot)

Where ∝ are the temperature coefficient of resistivity and its unit is k-1.

Using R = (ρL/A) we can prove that:

∝ = (ρt – ρo)/( ρot)

  1. Positive temperature co-efficient: If the value of resistance increases with the rise in temperature then α is positive.
  2. Negative temperature co-efficient: If the value of resistance decreases with a rise in temperature then α is negative. Example: Germanium & Silicon.


Resiprocal of resistivity is called conductivity like wise resiprocal resistance is called conductance.

Conductance = 1/Resistance

Also, σ = 1/ρ  ;  Conductivity = 1/Resistivity

Unit: SI-unit of conductivity is:

1/(ohm.m) = ohm-1.m-1 = mho.m-1

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